Computing free energy is a fundamental problem in statistical physics.Recently,two distinct methods have been developed and have demonstrated remarkable success:the tensor-network-based contraction method and the neur...Computing free energy is a fundamental problem in statistical physics.Recently,two distinct methods have been developed and have demonstrated remarkable success:the tensor-network-based contraction method and the neural-network-based variational method.Tensor networks are accurate,but their application is often limited to low-dimensional systems due to the high computational complexity in high-dimensional systems.The neural network method applies to systems with general topology.However,as a variational method,it is not as accurate as tensor networks.In this work,we propose an integrated approach,tensor-network-based variational autoregressive networks(TNVAN),that leverages the strengths of both tensor networks and neural networks:combining the variational autoregressive neural network’s ability to compute an upper bound on free energy and perform unbiased sampling from the variational distribution with the tensor network’s power to accurately compute the partition function for small sub-systems,resulting in a robust method for precisely estimating free energy.To evaluate the proposed approach,we conducted numerical experiments on spin glass systems with various topologies,including two-dimensional lattices,fully connected graphs,and random graphs.Our numerical results demonstrate the superior accuracy of our method compared to existing approaches.In particular,it effectively handles systems with longrange interactions and leverages GPU efficiency without requiring singular value decomposition,indicating great potential in tackling statistical mechanics problems and simulating high-dimensional complex systems through both tensor networks and neural networks.展开更多
Constraint satisfaction problems(CSPs)are a class of problems that are ubiquitous in science and engineering.They feature a collection of constraints specified over subsets of variables.A CSP can be solved either dire...Constraint satisfaction problems(CSPs)are a class of problems that are ubiquitous in science and engineering.They feature a collection of constraints specified over subsets of variables.A CSP can be solved either directly or by reducing it to other problems.This paper introduces the Julia ecosystem for solving and analyzing CSPs with a focus on the programming practices.We introduce some important CSPs and show how these problems are reduced to each other.We also show how to transform CSPs into tensor networks,how to optimize the tensor network contraction orders,and how to extract the solution space properties by contracting the tensor networks with generic element types.Examples are given,which include computing the entropy constant,analyzing the overlap gap property,and the reduction between CSPs.展开更多
The polaron problem is a very old problem in condensed matter physics that dates back to the thirties,but still remains largely unsolved today,especially when electron–electron interaction is taken into consideration...The polaron problem is a very old problem in condensed matter physics that dates back to the thirties,but still remains largely unsolved today,especially when electron–electron interaction is taken into consideration.The presence of both electron–electron and electron–phonon interactions in the problem invalidates most existing numerical methods,which are either computationally too expensive or simply intractable.The continuous-time quantum Monte Carlo(CTQMC)methods could tackle this problem,but they are only effective on the imaginarytime axis.In this work,we present a method based on tensor networks and the path integral formalism to solve polaron impurity problems.As both the electron and phonon baths can be integrated out via the Feynman–Vernon influence functional in the path integral formalism,our method is free of bath discretization error.It can also flexibly work on imaginary time,Keldysh contour,and L-shaped Kadanoff contour.In addition,our method can naturally resolve several long-existing challenges:(i)non-diagonal hybridization function;(ii)measuring multi-time correlations beyond single-particle Green’s functions.We demonstrate the effectiveness and accuracy of our method with extensive numerical examples against analytic solutions,exact diagonalization,and CTQMC.We also perform full-fledged real-time calculations that have never been done before to our knowledge,which could serve as a benchmarking baseline for future method developments.展开更多
We propose a generalized Lanczos method to generate the many-body basis states of quantum lattice models using tensor-network states （TNS）. The ground-state wave function is represented as a linear superposition com...We propose a generalized Lanczos method to generate the many-body basis states of quantum lattice models using tensor-network states （TNS）. The ground-state wave function is represented as a linear superposition composed from a set of TNS generated by Lanczos iteration. This method improves significantly the accuracy of the tensor-network algorithm and provides an effective way to enlarge the maximal bond dimension of TNS. The ground state such obtained contains significantly more entanglement than each individual TNS, reproducing correctly the logarithmic size dependence of the entanglement entropy in a critical system. The method can be generalized to non-Hamiltonian systems and to the calculation of low-lying excited states, dynamical correlation functions, and other physical properties of strongly correlated systems.展开更多
Tensor networks are used to describe the ground state wavefunction of the quantum many-body system.Recently,it has been shown that a tensor network can generate the anti-de Sitter(AdS)geometry by using the entanglemen...Tensor networks are used to describe the ground state wavefunction of the quantum many-body system.Recently,it has been shown that a tensor network can generate the anti-de Sitter(AdS)geometry by using the entanglement renormalization approach,which provides a new way to realize bulk reconstruction in the AdS/conformal field theory correspondence.However,whether the dynamical connections can be found between the tensor network and gravity is an important unsolved problem.In this paper,we give a novel proposal to integrate ideas from tensor networks,entanglement entropy,canonical quantization of quantum gravity and the holographic principle and argue that the gravitational dynamics can be generated from a tensor network if the wave function of the latter satisfies the Wheeler–DeWitt equation.展开更多
The prediction of the intensity of tropical cyclones(TCs)is crucial for weather forecasts and disaster prevention.Maximum sustained wind(MSW)is one of the main indexes of TC intensity.Analyzing multispectral images(MS...The prediction of the intensity of tropical cyclones(TCs)is crucial for weather forecasts and disaster prevention.Maximum sustained wind(MSW)is one of the main indexes of TC intensity.Analyzing multispectral images(MSIs)of cyclones by deep learning methods can increase MSW accuracy.However,existing methods are mostly designed for infrared images,not being able to leverage different band data or represent the rich temporal-spectral-spatial features in MSIs.Meanwhile,MSIs alone cannot provide all the necessary or accurate information of TCs as there are usually undesired variations or distortions in TC structures reflected by the images due to the uniqueness of each TC and positions of TCs and the satellites that capture images.Moreover,TC formation and evolution are affected by various physical factors that are not recorded in MSIs or cannot be easily derived from the images.To perform multimodal data fusion while making use of the most valuable information,we propose a novel model,Invalid-Band-Suppressed and Structure-Descriptor-Enhanced Temporal Tensor Network(ISSDTN).ISSDTN extracts features from the long-wavelength and the short-wavelength band images of each set of TC MSIs in two separate paths to suppress invalid band data.Finally,the paths are combined to fuse the multimodal information,i.e.,image features and Structure Descriptors(SDs)via cross-attentions to predict MSW.Experimental results show that ISSDTN outperforms many baselines and state-of-the-art methods in various cyclone datasets.The errors of 24 h MSW prediction by ISSDTN is as low as 4.49 m/s and 5.33 m/s for FY4A-TC and TCIR datasets,respectively.展开更多
Dear Editor,This letter proposes the graph tensor alliance attention network(GT-A^(2)T)to represent a dynamic graph(DG)precisely.Its main idea includes 1)Establishing a unified spatio-temporal message propagation fram...Dear Editor,This letter proposes the graph tensor alliance attention network(GT-A^(2)T)to represent a dynamic graph(DG)precisely.Its main idea includes 1)Establishing a unified spatio-temporal message propagation framework on a DG via the tensor product for capturing the complex cohesive spatio-temporal interdependencies precisely and 2)Acquiring the alliance attention scores by node features and favorable high-order structural correlations.展开更多
The Ryu-Takayanagi(RT)formula plays a large role in the current theory of gauge-gravity duality and emergent geometry phenomena.The recent reinterpretation of this formula in terms of a set of"bit threads"is...The Ryu-Takayanagi(RT)formula plays a large role in the current theory of gauge-gravity duality and emergent geometry phenomena.The recent reinterpretation of this formula in terms of a set of"bit threads"is an interesting effort in understanding holography.In this study,we investigate a quantum generalization of the"bit threads"based on a tensor network,with particular focus on the multi-scale entanglement renormalization ansatz(MERA).We demonstrate that,in the large c limit,isometries of the MERA can be regarded as"sources"(or"sinks")of the information flow,which extensively modifies the original picture of bit threads by introducing a new variableρ:density of the isometries.In this modified picture of information flow,the isometries can be viewed as generators of the flow.The strong subadditivity and related properties of the entanglement entropy are also obtained in this new picture.The large c limit implies that classical gravity can emerge from the information flow.展开更多
This paper investigates the networked evolutionary model based on snow-drift game with the strategy of rewards and penalty. Firstly, by using the semi-tensor product of matrices approach, the mathematical model of the...This paper investigates the networked evolutionary model based on snow-drift game with the strategy of rewards and penalty. Firstly, by using the semi-tensor product of matrices approach, the mathematical model of the networked evolutionary game is built. Secondly, combined with the matrix expression of logic, the mathematical model is expressed as a dynamic logical system and next converted into its evolutionary dynamic algebraic form. Thirdly, the dynamic evolution process is analyzed and the final level of cooperation is discussed. Finally, the effects of the changes in the rewarding and penalty factors on the level of cooperation in the model are studied separately, and the conclusions are verified by examples.展开更多
This article discusses the covariance correlation tensor (CCT) in quantum network theory for four Bell bases in detail. Furthermore, it gives the expression of the density operator in terms of CCT for a quantum networ...This article discusses the covariance correlation tensor (CCT) in quantum network theory for four Bell bases in detail. Furthermore, it gives the expression of the density operator in terms of CCT for a quantum network of three nodes, thus gives the criterion of entanglement for this case, i.e. the conditions of complete separability and partial separability for a given quantum state of three bodies. Finally it discusses the general case for the quantum network of nodes.展开更多
This paper investigates epidemic dynamics over dynamic networks via the approach of semi-tensor product of matrices. First, a formal susceptible-infected-susceptible epidemic dynamic model over dynamic networks （SISE...This paper investigates epidemic dynamics over dynamic networks via the approach of semi-tensor product of matrices. First, a formal susceptible-infected-susceptible epidemic dynamic model over dynamic networks （SISED-DN） is given. Second, based on a class of determinate co-evolutionary rule, the matrix expressions are established for the dynamics of individual states and network topologies, respectively. Then, all possible final spreading equilibria are obtained for any given initial epidemic state and network topology by the matrix expression. Third, a sufficient and necessary condition of the existence of state feedback vaccination control is presented to make every individual susceptible. The study of illustrative examples shows the effectiveness of our new results.展开更多
This article discusses the separability of the pure states and mixed states of the quantum network of two nodes by means of the criterion of no entanglement in terms of the covariance correlation tensor in quantum net...This article discusses the separability of the pure states and mixed states of the quantum network of two nodes by means of the criterion of no entanglement in terms of the covariance correlation tensor in quantum network theory, i.e. for a composite system consisting of two nodes. The covariance correlation tensor is equal to zero for all possible and .展开更多
In this paper, we propose a new centrality algorithm that can simultaneously rank the nodes and layers of multilayer networks, referred to as the MRFNL centrality. The centrality of nodes and layers are obtained by de...In this paper, we propose a new centrality algorithm that can simultaneously rank the nodes and layers of multilayer networks, referred to as the MRFNL centrality. The centrality of nodes and layers are obtained by developing a novel iterative algorithm for computing a set of tensor equations. Under some conditions, the existence and uniqueness of this centrality were proven by applying the Brouwer fixed point theorem. Furthermore, the convergence of the proposed iterative algorithm was established. Finally, numerical experiments on a simple multilayer network and two real-world multilayer networks(i.e., Pierre Auger Collaboration and European Air Transportation Networks) are proposed to illustrate the effectiveness of the proposed algorithm and to compare it to other existing centrality measures.展开更多
Using the semi-tensor product method, this paper investigates the modeling and analysis of networked evolutionary games(NEGs) with finite memories, and presents a number of new results. Firstly, a kind of algebraic ex...Using the semi-tensor product method, this paper investigates the modeling and analysis of networked evolutionary games(NEGs) with finite memories, and presents a number of new results. Firstly, a kind of algebraic expression is formulated for the networked evolutionary games with finite memories, based on which the behavior of the corresponding evolutionary game is analyzed. Secondly, under a proper assumption, the existence of Nash equilibrium of the given networked evolutionary games is proved and a free-type strategy sequence is designed for the convergence to the Nash equilibrium. Finally, an illustrative example is worked out to support the obtained new results.展开更多
基金supported by Projects 12325501,12047503,and 12247104 of the National Natural Science Foundation of ChinaProject ZDRW-XX-2022-3-02 of the Chinese Academy of Sciencessupported by the Innovation Program for Quantum Science and Technology project 2021ZD0301900。
文摘Computing free energy is a fundamental problem in statistical physics.Recently,two distinct methods have been developed and have demonstrated remarkable success:the tensor-network-based contraction method and the neural-network-based variational method.Tensor networks are accurate,but their application is often limited to low-dimensional systems due to the high computational complexity in high-dimensional systems.The neural network method applies to systems with general topology.However,as a variational method,it is not as accurate as tensor networks.In this work,we propose an integrated approach,tensor-network-based variational autoregressive networks(TNVAN),that leverages the strengths of both tensor networks and neural networks:combining the variational autoregressive neural network’s ability to compute an upper bound on free energy and perform unbiased sampling from the variational distribution with the tensor network’s power to accurately compute the partition function for small sub-systems,resulting in a robust method for precisely estimating free energy.To evaluate the proposed approach,we conducted numerical experiments on spin glass systems with various topologies,including two-dimensional lattices,fully connected graphs,and random graphs.Our numerical results demonstrate the superior accuracy of our method compared to existing approaches.In particular,it effectively handles systems with longrange interactions and leverages GPU efficiency without requiring singular value decomposition,indicating great potential in tackling statistical mechanics problems and simulating high-dimensional complex systems through both tensor networks and neural networks.
基金funded by the National Key R&D Program of China(Grant No.2024YFE0102500)the National Natural Science Foundation of China(Grant No.12404568)+1 种基金the Guangzhou Municipal Science and Technology Project(Grant No.2023A03J00904)the Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area,China and the Undergraduate Research Project from HKUST(Guangzhou).
文摘Constraint satisfaction problems(CSPs)are a class of problems that are ubiquitous in science and engineering.They feature a collection of constraints specified over subsets of variables.A CSP can be solved either directly or by reducing it to other problems.This paper introduces the Julia ecosystem for solving and analyzing CSPs with a focus on the programming practices.We introduce some important CSPs and show how these problems are reduced to each other.We also show how to transform CSPs into tensor networks,how to optimize the tensor network contraction orders,and how to extract the solution space properties by contracting the tensor networks with generic element types.Examples are given,which include computing the entropy constant,analyzing the overlap gap property,and the reduction between CSPs.
基金supported by the National Natural Science Foundation of China(Grant No.12104328)。
文摘The polaron problem is a very old problem in condensed matter physics that dates back to the thirties,but still remains largely unsolved today,especially when electron–electron interaction is taken into consideration.The presence of both electron–electron and electron–phonon interactions in the problem invalidates most existing numerical methods,which are either computationally too expensive or simply intractable.The continuous-time quantum Monte Carlo(CTQMC)methods could tackle this problem,but they are only effective on the imaginarytime axis.In this work,we present a method based on tensor networks and the path integral formalism to solve polaron impurity problems.As both the electron and phonon baths can be integrated out via the Feynman–Vernon influence functional in the path integral formalism,our method is free of bath discretization error.It can also flexibly work on imaginary time,Keldysh contour,and L-shaped Kadanoff contour.In addition,our method can naturally resolve several long-existing challenges:(i)non-diagonal hybridization function;(ii)measuring multi-time correlations beyond single-particle Green’s functions.We demonstrate the effectiveness and accuracy of our method with extensive numerical examples against analytic solutions,exact diagonalization,and CTQMC.We also perform full-fledged real-time calculations that have never been done before to our knowledge,which could serve as a benchmarking baseline for future method developments.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11190024 and 11474331)
文摘We propose a generalized Lanczos method to generate the many-body basis states of quantum lattice models using tensor-network states （TNS）. The ground-state wave function is represented as a linear superposition composed from a set of TNS generated by Lanczos iteration. This method improves significantly the accuracy of the tensor-network algorithm and provides an effective way to enlarge the maximal bond dimension of TNS. The ground state such obtained contains significantly more entanglement than each individual TNS, reproducing correctly the logarithmic size dependence of the entanglement entropy in a critical system. The method can be generalized to non-Hamiltonian systems and to the calculation of low-lying excited states, dynamical correlation functions, and other physical properties of strongly correlated systems.
基金supported by the National Natural Science Foundation of China under Grant No.11675272supported by China Postdoctoral Science Foundation(No.2019M653137)。
文摘Tensor networks are used to describe the ground state wavefunction of the quantum many-body system.Recently,it has been shown that a tensor network can generate the anti-de Sitter(AdS)geometry by using the entanglement renormalization approach,which provides a new way to realize bulk reconstruction in the AdS/conformal field theory correspondence.However,whether the dynamical connections can be found between the tensor network and gravity is an important unsolved problem.In this paper,we give a novel proposal to integrate ideas from tensor networks,entanglement entropy,canonical quantization of quantum gravity and the holographic principle and argue that the gravitational dynamics can be generated from a tensor network if the wave function of the latter satisfies the Wheeler–DeWitt equation.
基金supported by the National Natural Science Foundation of China under Grant 61702094 and the DHU Distinguished Young Professor Program under Grant LZB2025003.
文摘The prediction of the intensity of tropical cyclones(TCs)is crucial for weather forecasts and disaster prevention.Maximum sustained wind(MSW)is one of the main indexes of TC intensity.Analyzing multispectral images(MSIs)of cyclones by deep learning methods can increase MSW accuracy.However,existing methods are mostly designed for infrared images,not being able to leverage different band data or represent the rich temporal-spectral-spatial features in MSIs.Meanwhile,MSIs alone cannot provide all the necessary or accurate information of TCs as there are usually undesired variations or distortions in TC structures reflected by the images due to the uniqueness of each TC and positions of TCs and the satellites that capture images.Moreover,TC formation and evolution are affected by various physical factors that are not recorded in MSIs or cannot be easily derived from the images.To perform multimodal data fusion while making use of the most valuable information,we propose a novel model,Invalid-Band-Suppressed and Structure-Descriptor-Enhanced Temporal Tensor Network(ISSDTN).ISSDTN extracts features from the long-wavelength and the short-wavelength band images of each set of TC MSIs in two separate paths to suppress invalid band data.Finally,the paths are combined to fuse the multimodal information,i.e.,image features and Structure Descriptors(SDs)via cross-attentions to predict MSW.Experimental results show that ISSDTN outperforms many baselines and state-of-the-art methods in various cyclone datasets.The errors of 24 h MSW prediction by ISSDTN is as low as 4.49 m/s and 5.33 m/s for FY4A-TC and TCIR datasets,respectively.
基金supported in part by the National Natural Science Foundation of China(62372385).
文摘Dear Editor,This letter proposes the graph tensor alliance attention network(GT-A^(2)T)to represent a dynamic graph(DG)precisely.Its main idea includes 1)Establishing a unified spatio-temporal message propagation framework on a DG via the tensor product for capturing the complex cohesive spatio-temporal interdependencies precisely and 2)Acquiring the alliance attention scores by node features and favorable high-order structural correlations.
基金Supported in part by the National Natural Science Foundation of China(11975116,11665016,11563006)Jiangxi Science Foundation for Distinguished Young Scientists(20192BCB23007)。
文摘The Ryu-Takayanagi(RT)formula plays a large role in the current theory of gauge-gravity duality and emergent geometry phenomena.The recent reinterpretation of this formula in terms of a set of"bit threads"is an interesting effort in understanding holography.In this study,we investigate a quantum generalization of the"bit threads"based on a tensor network,with particular focus on the multi-scale entanglement renormalization ansatz(MERA).We demonstrate that,in the large c limit,isometries of the MERA can be regarded as"sources"(or"sinks")of the information flow,which extensively modifies the original picture of bit threads by introducing a new variableρ:density of the isometries.In this modified picture of information flow,the isometries can be viewed as generators of the flow.The strong subadditivity and related properties of the entanglement entropy are also obtained in this new picture.The large c limit implies that classical gravity can emerge from the information flow.
文摘This paper investigates the networked evolutionary model based on snow-drift game with the strategy of rewards and penalty. Firstly, by using the semi-tensor product of matrices approach, the mathematical model of the networked evolutionary game is built. Secondly, combined with the matrix expression of logic, the mathematical model is expressed as a dynamic logical system and next converted into its evolutionary dynamic algebraic form. Thirdly, the dynamic evolution process is analyzed and the final level of cooperation is discussed. Finally, the effects of the changes in the rewarding and penalty factors on the level of cooperation in the model are studied separately, and the conclusions are verified by examples.
文摘This article discusses the covariance correlation tensor (CCT) in quantum network theory for four Bell bases in detail. Furthermore, it gives the expression of the density operator in terms of CCT for a quantum network of three nodes, thus gives the criterion of entanglement for this case, i.e. the conditions of complete separability and partial separability for a given quantum state of three bodies. Finally it discusses the general case for the quantum network of nodes.
基金This work was supported by the National Natural Science Foundation of China （Nos. 61374065, 61503225）, the Research Fund for the Taishan Scholar Project of Shandong Province, and the Natural Science Foundation of Shandong Province （No. ZR2015FQ003）.
文摘This paper investigates epidemic dynamics over dynamic networks via the approach of semi-tensor product of matrices. First, a formal susceptible-infected-susceptible epidemic dynamic model over dynamic networks （SISED-DN） is given. Second, based on a class of determinate co-evolutionary rule, the matrix expressions are established for the dynamics of individual states and network topologies, respectively. Then, all possible final spreading equilibria are obtained for any given initial epidemic state and network topology by the matrix expression. Third, a sufficient and necessary condition of the existence of state feedback vaccination control is presented to make every individual susceptible. The study of illustrative examples shows the effectiveness of our new results.
文摘This article discusses the separability of the pure states and mixed states of the quantum network of two nodes by means of the criterion of no entanglement in terms of the covariance correlation tensor in quantum network theory, i.e. for a composite system consisting of two nodes. The covariance correlation tensor is equal to zero for all possible and .
基金Project supported by the Postgraduate Research and Practice Innovation Program of Jiangsu Province,China(Grant No.AE91313/001/016)the National Natural Science Foundation of China(Grant No.11701097)the Natural Science Foundation of Jiangxi Province,China(Grant No.20161BAB212055)
文摘In this paper, we propose a new centrality algorithm that can simultaneously rank the nodes and layers of multilayer networks, referred to as the MRFNL centrality. The centrality of nodes and layers are obtained by developing a novel iterative algorithm for computing a set of tensor equations. Under some conditions, the existence and uniqueness of this centrality were proven by applying the Brouwer fixed point theorem. Furthermore, the convergence of the proposed iterative algorithm was established. Finally, numerical experiments on a simple multilayer network and two real-world multilayer networks(i.e., Pierre Auger Collaboration and European Air Transportation Networks) are proposed to illustrate the effectiveness of the proposed algorithm and to compare it to other existing centrality measures.
基金supported by the National Natural Science Foundation of China(61503225)the Natural Science Foundation of Shandong Province(ZR2015FQ003,ZR201709260273)
文摘Using the semi-tensor product method, this paper investigates the modeling and analysis of networked evolutionary games(NEGs) with finite memories, and presents a number of new results. Firstly, a kind of algebraic expression is formulated for the networked evolutionary games with finite memories, based on which the behavior of the corresponding evolutionary game is analyzed. Secondly, under a proper assumption, the existence of Nash equilibrium of the given networked evolutionary games is proved and a free-type strategy sequence is designed for the convergence to the Nash equilibrium. Finally, an illustrative example is worked out to support the obtained new results.
